# Value of log 125 base root 5

The value of log 125 base root 5 is equal to 6, that is, log√5125 = 6. In this post, we will learn how to find the logarithm of 125 when the base is √5.

## How to Find log125 Base Root 5

Question: What is log125 base√5?

Answer: log125 base root 5 equals 6.

Solution:

Step 1:

We know that 125 is a product of three numbers of 5’s. In other words, we can write 125 as follows.

125 = 5×5×5

⇒ 125 = 53 …(∗)

Next, we write 5 as a power of √5.

5 = (√5)2

Thus, Equation (∗) can be rewritten as

125 = [(√5)2]3

∴ 125 = (√5)6 by the indices rule amn = (am)n

Step 2:

Now, we will take logarithms with base √5 on both sides. This will give us

log√5125 = log√5(√5)6

⇒ log√5125 = 6 log√5(√5)

⇒ log√5125 = 6, as we know the logarithm formula: logaa = 1.

Hence the value of log 125 base root 5 is 6.

log 8 base 2

log 16 base 2

log 16 base 4

log 16 base √2

## FAQs

### Q1: What is log 125 with base root 5?

Answer: As 125=(√5)6, the value of the log125 with base root 5 is equal to 6.